Final answer:
The two shapes described in the clues are the Square and the Rhombus.
Step-by-step explanation:
The two shapes that meet all the given criteria are the Square and the Rhombus.
A Square has all sides equal in length, 4 sides, and 2 pairs of parallel sides.
A Rhombus also has all sides equal in length, 4 sides, and 2 pairs of parallel sides.